The generator matrix

 1  0  0  1  1  1  X  0  1  1  1  X  2  1 X+2 X+2  1  1  2  1  1  1  1  0  X  0  1 X+2  1  1  2  1 X+2  0  1  X  1  1  1  1 X+2  0  1  1  2  X  1  1  X X+2  0  1  1  1  1  2  2 X+2  1  1  1  1  1  1  1  1  1
 0  1  0  0  1 X+3  1  1  X X+2  1  1  2  1  X  1 X+1 X+2  1 X+2 X+1 X+3 X+2  1  2  X X+2  1 X+3  2  1  3  1  1 X+1  2  2 X+3 X+3  X  1  1  2 X+1  X  1  3  1  1  1  1 X+2  X  3  2  1  1  1  0  0  1  2 X+2 X+3 X+1 X+2 X+1
 0  0  1  1  1  0  1 X+1 X+1  2  0  2  1 X+1  1  0  0 X+3  1  X X+3  X X+1 X+2  1  1 X+2 X+1 X+1  0  1  X  1 X+2  3  1  1  3  2  0 X+1  X  2 X+2  1 X+3 X+2  X  0 X+3  3  1  X X+1  X X+2  0  1 X+1  X  X  3 X+1 X+2 X+2  X  2
 0  0  0  X  0 X+2  2  0  X  0 X+2 X+2  X  2 X+2  0  2  2  X  X  X  2  0 X+2 X+2  2  0 X+2  0  X  2  X  X X+2  X X+2  2  0  0  2  0  2 X+2 X+2 X+2  2  0  2 X+2  2  X X+2 X+2  2  X  X  2 X+2  X X+2  X  0  0  2  X  0 X+2
 0  0  0  0  2  0  2  0  2  2  2  0  0  0  2  2  2  0  2  0  0  0  2  2  0  2  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  0  2  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+318x^60+152x^61+840x^62+336x^63+957x^64+368x^65+1142x^66+388x^67+974x^68+372x^69+856x^70+248x^71+561x^72+120x^73+290x^74+52x^75+121x^76+12x^77+36x^78+41x^80+4x^82+3x^84

The gray image is a code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.16 in 26.7 seconds.